Motion in One Dimension with Air Drag

Purpose: To analyze how changing force affects motion in one dimension.

Introduction Questions:
1) By unit analysis, show that the above equation (Vnew = Vold +aavg*delta(t)) is valid.

m/s = m/s + (m/s^2)*s = m/s

2) Why do we use aavg in equation (1)?

- We assume that acceleration is changing

3) Come up with an analogous equation relating Ynew to Yold.

Ynew = Yold + deltaY

4) What is the benifit of choosing a small delta t?

- For more accuracy

Questions: Fd = -kv (where k is a proportionality constant)

1) Draw a detailed motion diagram of the object falling down.

1a) Now draw a force diagram for the object falling down. Include vectors for all forces, and write a statement of Newton's Second Law. Solve for the acceleration.               Force Diagram

- For every action there is an equal and opposite reaction.

Fnet = Fd - Fg

ma = Fd - Fg

a = (Fd - Fg)/m

a = (-kv - mg)/m

a = (-kv)/m - g

1b) Give the condition for the object at terminal velocity (hit: a = 0). Using the condition solve for k.

0 = (-kv)/m - g

g = -kv/m

mg = -kv

k = -mg/v(terminal)

1c) Substitue k into your expression for the acceleration from part a.

a = -(-gm/v(terminal))v/m - g

a = gv/v(terminal) - g

a = -g(v/v(terminal) +1)

2a) What are the assumptions?

- t = 0 s

- g = 9.8 m/s^2

- v = 100 m/s

- r = 1000 m

- v (terminal) = 40 m/s

- delta t = .1 s

2b) What is v-halfstep?

- Taking the average velocity at two times to find the actual velocity

2c) What is a-halfstep?

- Taking the average acceleration at two times to find the actual acceleration

3) Using the graph paper provided, draw scaled graphs of position vs. time, velocity vs. time, and acceleration vs. time for the object, first assuming no air drag. Make predictions on another sheet of paper about how position and velocity would change if you include air drag.

The position vs. time graph that we predicted is very similar to the actual position vs. time graph. However, the velocity vs. time graph that we predicted is no where near the actual graph. I believe that we accounted for drag wrong and we predicted the graph without drag wrong too.

Now look at a drag force that is dependent on the square of the velocity. Assuming a drag force, Fd = |kv^2|, find the new formula for the acceleration.

Conclusion: This lab was complicated. Even though we did it more as a class, it was still difficult. There could have been a lot of different kinds of error. The fact that most of us didn't really understand it, is cause for a lot of error. I think the only way to do better on this lab is to do it over again.